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0542-4320

Fluid mechanics 2

Also listed as: מכניקת הזורמים 2

Differential fluid mechanics done properly: Navier–Stokes derived rather than quoted, potential flow, boundary layers, and a first look at turbulence. The gateway to every fluids group in the school.

Semester
Semester B
Weekly hours
4h
Counts as
Core: fluids
Interest areas
Flow and thermal design · Aeronautics and space

What it covers

Kinematics and the governing equations

  • Material derivative, deformation and rotation tensors, vorticity, circulation
  • Reynolds transport theorem
  • Differential conservation laws and the Newtonian constitutive law
  • Exact solutions: Couette, Poiseuille, Stokes first and second problems
  • Dimensional analysis and similitude, Buckingham Pi, Re, Fr, We, Ma, Eu

Potential flow and boundary layers

  • Velocity potential and stream function
  • Elementary flows and superposition: source, sink, doublet, vortex
  • Flow over a cylinder, d'Alembert's paradox, Kutta–Joukowski lift
  • Prandtl boundary-layer equations, Blasius and Falkner–Skan solutions
  • Momentum-integral method, separation, drag

Vorticity and transition

  • Vorticity dynamics, Kelvin's theorem, Helmholtz theorems
  • Transition to turbulence, Reynolds stresses, mixing length
  • Introduction to compressible flow as a bridge to gas dynamics

Results worth carrying out

  • Navier–Stokes

    ρDuDt=p+μ2u+ρg\rho\frac{D\mathbf{u}}{Dt} = -\nabla p + \mu\nabla^2\mathbf{u} + \rho\mathbf{g}
  • Potential flow

    2ϕ=0\nabla^2\phi = 0
  • Kutta–Joukowski

    Γ=udl,L=ρUΓ\Gamma = \oint \mathbf{u}\cdot d\mathbf{l}, \qquad L' = \rho U_\infty \Gamma
  • Blasius boundary layer

    δx5Rex\frac{\delta}{x} \approx \frac{5}{\sqrt{\mathrm{Re}_x}}

Figures worth knowing

  • Streamline and streakline plots
  • Potential against real flow over a cylinder
  • Boundary-layer profile and separation sketch
  • von Kármán vortex street

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